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mattst88
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Homework Statement
If linearly dependent, write one matrix as a linear combination of the rest.
[tex]\left[\begin{array}{cc} 1&1 \\ 2&1 \end{array}\right][/tex] [tex]\left[\begin{array}{cc} 1&0 \\ 0&2 \end{array}\right][/tex] [tex]\left[\begin{array}{cc} 0&3 \\ 2&1 \end{array}\right][/tex] [tex]\left[\begin{array}{cc} 4&6 \\ 8&6 \end{array}\right][/tex]
Homework Equations
The Attempt at a Solution
Choosing coefficients a, b, c, d for the matrices, respectively, I set up 4 equations and 4 unknowns:
row 1 column 1: [tex]a + b + 4d = 0[/tex]
row 1 column 2: [tex]a+ 3c + 6d = 0[/tex]
row 2 column 1: [tex]2a + 2c + 8d = 0[/tex]
row 2 column 2: [tex]a + 2b + c + 6d = 0[/tex]
From this, I create a 4x5 matrix and using Gauss-Jordan elimination arrive at:
Edit: this is wrong. See below
[tex]\left[\begin{array}{ccccc}
1&0&0&2&0 \\
0&1&0&2&0 \\
0&0&1&\frac{4}{3}&0 \\
0&0&0&0&0 \end{array}\right][/tex]
From this, it is clear that the 4 matrices are linearly dependent.
What I do not understand: how do I, given this last matrix, write one of the matrices as a linear combination of the others?
Thanks
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